Chimera states in coupled Kuramoto oscillators with inertia

TL;DR

This paper investigates chimera states in coupled Kuramoto oscillators with inertia, revealing how inertia influences the transition from quasi-periodic to chaotic behaviors and identifying new chaotic chimera solutions with broken symmetry.

Contribution

It introduces novel chaotic chimera states in inertial Kuramoto oscillators and analyzes their lifetime scaling and intermittent dynamics, expanding understanding of synchronization phenomena.

Findings

At small inertia, mainly quasi-periodic chimeras are observed.

At large inertia, chaotic solutions with broken symmetry emerge.

Intermittent chaotic chimeras have lifetimes scaling as a power-law with system size.

Abstract

The dynamics of two symmetrically coupled populations of rotators is studied for different values of the inertia. The system is characterized by different types of solutions, which all coexist with the fully synchronized state. At small inertia the system is no more chaotic and one observes mainly quasi- periodic chimeras, while the usual (stationary) chimera state is not anymore observable. At large inertia one observes two different kind of chaotic solutions with broken symmetry: the intermittent chaotic chimera, characterized by a synchronized population and a population displaying a turbulent behaviour, and a second state where the two populations are both chaotic but whose dynamics adhere to two different macroscopic attractors. The intermittent chaotic chimeras are characterized by a finite life-time, whose duration increases as a power-law with the system size and the inertia value. Moreover, the chaotic population exhibits clear intermittent behavior, displaying a laminar phase where the two populations tend to synchronize, and a turbulent phase where the macroscopic motion of one population is definitely erratic. In the thermodynamic limit these states survive for infinite time and the laminar regimes tends to disappear, thus giving rise to stationary chaotic solutions with broken symmetry contrary to what observed for chaotic chimeras on a ring geometry.